I can tell this is from a book you are reading. It means that while people were busy doing something else a pot of soup bubbled away on the stove in the background. The phrase is used to create an image or setting in the back ground.

I don't think the soup spilled over and if this is a book then the comment on the soup was just something in the background to make reference to. The comment about the soup probably was meant to show how someone or some people had something more important to do. Like if the person cooking had a romantic visitor and they forgot about the soup!!!
I am sure they would have turned it off later.